I'm surprised no one made this thread yet.
ALDS Series 1 - Angels vs. Red Sox
Beckett dominated game one, and has now pitched 18 consecutive scoreless innings in the playoffs (yay caring over stats from 2003.) The Angels are beat up, have a weak defense, and less than stellar pitching. They also haven't faced Matsuzaka before. Anaheim might steal a game, but I don't see this one going past 4 games.
ALDS Series 2 - Yankees vs. Indians
Cleveland has a 1-2 punch of Cy Young contenders, a fairly potent offense, and possibly the best set-up guy in the game right now. There's no way of knowing what you'll get from their closer, and that could become an issue. The Yankees have a monster line up, decent starters, and an incredibly strong back end of their bullpen. I think Cleveland's starting pitchers will end up winning the series for them, but it really could go either way. I certainly don't expect them to take these games by nine runs like they did tonight.
NLDS Series 1 - Rockies vs. Phillies
The Rockies are the hottest team in the playoffs, hands down. They won 14 of their last 15 games getting into the playoffs, and they did it with pitching instead of the typical Rockies slugging style. The Phillies simply don't have a pitching staff strong enough to win in the postseason. The Rockies should take this one easily, especially being up by two games and heading back to Colorado.
NLDS Seris 2 - Cubs vs. Diamondbacks
The Cubs came out of the NL Central, the only division in baseball with six teams. Of course, none of those six seemed interested in winning baseball games this year. The Diamondbacks are probably the strongest team coming out of the NL this year, and they should handle the Cubs soundly. *Insert Pinella-is-being-paid-off conspiracy theory here.*
ALCS - TBA
As an unappologetic Red Sox fan, I think they have a good shot of making the World Series. The ALCS is certainly going to be a fantastic series this year, though. Boston, Cleveland, and New York are all strong teams that could come out on top. It really is a shame that the Angels had so many late-season injuries this year, because Mike Scocia is a marvelous manager and deserves a better showing than what his current roster will give him.
NLCS - TBA
An all NL West NLCS should be entertaining. The Rockies have to slow down at some point, don't they? Assuming it ends up being Rockies vs. D'backs, I'd have a hard time picking a favorite. I'll go with Colorado because Arizona's offense is just too inconsistant. If the Rockies' rotation can have good starts, then their offense should be more than sufficient to outscore their way to a World Series.
World Series - TBA
Well, I would say that the AL team will take this handily, but St. Louis proved me (and probably everyone outside of Missouri) wrong when I said that last year. That said, I still really like any of the AL teams' chances against the four remaining NL teams.